Abstract
Several dark energy experiments are available from a single large-area imaging survey and may be combined to improve cosmological parameter constraints and/or test inherent systematics. Two promising experiments are cosmic shear power spectra and counts of galaxy clusters. However, the two experiments probe the same cosmic mass density field in large-scale structure, therefore the combination may be less powerful than first thought.We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field. Fully taking into account the cross-covariance, as well as non-Gaussian errors on the lensing power spectrum covariance, we find a significant cross-correlation between the lensing power spectrum signals at multipoles l∼103 and the cluster counts containing halos with masses M≳1014 M⊙. Including the cross-covariance for the combined measurement degrades and in some cases improves the total signal-to-noise (S/N) ratios up to ∼±20% relative to when the two are independent. For cosmological parameter determination, the cross-covariance has a smaller effect as a result of working in a multi-dimensional parameter space, implying that the two observables can be considered independent to a good approximation. We also discuss the fact that cluster count experiments using lensing-selected mass peaks could be more complementary to cosmic shear tomography than mass-selected cluster counts of the corresponding mass threshold. Using lensing selected clusters with a realistic usable detection threshold ((S/N)cluster∼6 for a ground-based survey), the uncertainty on each dark energy parameter may be roughly halved by the combined experiments, relative to using the power spectra alone.
Highlights
We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field
We include the key parameters that may affect the observables within an adiabatic CDM dominated model with dark energy component: the density parameters are Ωde(= 0.73), Ωmh2(= 0.14), and Ωbh2(= 0.024); the primordial power spectrum parameters are the spectral tilt, ns(= 1), the running index, αs(= 0), and the normalization parameter of primordial curvature perturbation, δζ(= 5.07 × 10−5)
We use only the CMB information in the range of multipoles 10 ≤ l ≤ 2000, and we do not include the integrated Sachs-Wolfe (ISW) effect that contribute to the CMB spectra mainly at low multipoles l ∼< 10, because the ISW effect is very likely correlated with the cosmic shear power spectrum and cluster counts, and we will ignore the correlations in this paper
Summary
Dark energy are galaxy cluster counts and cosmic shear (e.g. [14]). Clusters of galaxies contain galaxies, hot gas and dark made in measuring the constituents of the universe The volumes will be large, and the deviation is small, this may amount to a significant uncertainty in the dark energy parameters as obtained by cluster counts, and dominates the non-Gaussian errors on the cosmic shear [45, 46, 47, 48]. One aspect of this cross-correlation was discussed in [49] and found to be negligible.
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